The decline curve analysis (DCA) technique is the simplest, fastest, least computationally demanding, and least data-required reservoir forecasting method. Assuming that the decline rate of the initial production data will continue in the future, the estimated ultimate recovery (EUR) can be determined at the end of the well/reservoir lifetime based on the declining mode. Many empirical DCA models have been developed to match different types of reservoirs as the decline rate varies from one well/reservoir to another. In addition to the uncertainties related to each DCA model’s performance, structure, and reliability, any of them can be used to estimate one deterministic value of the EUR, which, therefore, might be misleading with a bias of over- and/or under-estimation. To reduce the uncertainties related to the DCA, the EUR could be assumed to be within a certain range, with different levels of confidence. Probabilistic decline curve analysis (pDCA) is the method used to generate these confidence intervals (CIs), and many pDCA approaches have been introduced to reduce the uncertainties that come with the deterministic DCA. The selected probabilistic type of analysis (i.e., frequentist or Bayesian), the used DCA model(s), the type and the number of wells, the sampling technique of the data or the model’s parameters, and the parameters themselves undergo a probability distribution, and these are the main differences among all of these approaches and the factors that determine how each approach can quantify the uncertainties and mitigate them. In this work, the Bayesian and frequentist approaches are deeply discussed. In addition, the uncertainties of DCA are briefly discussed. Further, the bases of the different probabilistic analyses are explained. After that, 15 pDCA approaches are reviewed and summarized, and the differences among them are stated. The study concludes that Bayesian analysis is generally more effective than frequentist analysis, though with narrower CIs. However, the choice of DCA model and sampling algorithm can also affect the bounds of the CIs and the calculation of the EUR. Moreover, the pDCA approach is recommended for quantifying uncertainties in DCA, with narrower CIs that indicate greater effectiveness. However, the computational time and the number of iterations in sampling are also considered critical factors. That is why various assumptions and modifications have been made in the pDCA approaches, including the assumption of a certain probability distribution for the sampled parameters to improve their reliability of reserve estimation. The motivation behind this research was to present a full state-of-the-art review of the pDCA and the latest developments in this area of research.
Mud filtrate invasion is a vital parameter that should be optimized during drilling for oil and gas to reduce formation damage. Nanoparticles (NPs) have shown promising filtrate loss mitigation when used as drilling fluid (mud) additives in numerous recent studies. Modeling the influence of NPs can fasten the process of selecting their optimum type, size, concentration, etc. to meet the drilling conditions. In this study, a model was developed, using artificial neural network (ANN), to predict the filtrate invasion of nano-based mud under wide range of pressures and temperatures up to 500 psi and 350 °F, respectively. A total of 2,863 data points were used in the development of the model (806 data points were collected form conducted experiments and the rest were collected form the literature). Seven different types of NPs with size and concentration ranges from 15 to 50 nm and 0 to 2.5 wt%, respectively, had been included in the model to ensure universality. The dataset was divided into 70 % for training and 30 % for validation. A total of 6,750 different combinations for the model’s hyperparameters were evaluated to determine the optimum combination. The N-encoded method was used to convert the categorical data into numerical values. The model was evaluated through calculating the statistical parameters. The developed ANN-model proofed to be efficient in predicting the filtrate invasion at different pressures and temperatures with an average absolute relative error (AARE) of less than 0.5 % and a coefficient of determination (R2) of more than 0.99 for the overall data. The ANN-model covers wide range of pressures, temperatures as well as various NPs’ types, concentrations, and sizes, which confirms its useability and coverability. HIGHLIGHTS Artificial neural network (ANN)-model was developed to predict the volume of filtrate of water-based mud (WBM) modified with nanoparticles (NPs) A total of 2,863 data points were collected to build the ANN-model from both experimental work and literature considering 3 types of WBM modified with 7 types of NPs (SiO2, TiO2, Al2O3, CuO, MgO, ZnO, Fe2O3) with size and concentration ranges from 15 to 50 nm and 0 to 2.5 wt%, respectively, under wide range of pressures and temperatures up to 500 psi and 350 °F A total of 6,750 different combinations for the model’s hyperparameters were evaluated to determine the optimum combination and the N-encoded method was used to convert the categorical data into numerical values The ANN-model proofed to be efficient with an average absolute relative error (AARE) of less than 0.5 % and a coefficient of determination (R2) of more than 0.99 for the overall data GRAPHICAL ABSTRACT
During drilling of hydrocarbon reservoirs, loss of mud filtrate into the formations occurs due to the difference between mud hydrostatic and formation pressures. Filtrate invasion is a vital parameter that should be optimized to reduce formation damage. Recently, nanoparticles (NPs) — among different additives — have been thoroughly examined to minimize mud invasion and showed promising performance. Modeling the impact of NPs on the filtrate loss can fasten the process of selecting their optimum type, size, concentration, etc. to meet the drilling conditions. In this work, artificial neural network (ANN) was used to develop a model that can predict the filtrate invasion of nano-based mud under wide range of temperature and pressure up to 350 °F and 500 Psi, respectively. Seven types of nanoparticles with size and concentration ranges from 15 to 50 nm and 0 to 2.5 wt%, respectively, have been included in the model. Almost 2,863 data points were used to develop the ANN-model. Experimental work was conducted to collect 806 data points, whereas the rest were collected form the literature. The data set was divided into 70% for training and 30% for validating the model. A total of 6,750 different combinations for the model’s hyperparameters were evaluated to select the optimal combination. N-encoded method was used to convert the categorical data into numerical one. The model was evaluated through calculating the statistical parameters. The developed ANN-model showed high accuracy for predicting the filtrate loss at different pressures and temperatures. The obtained results showed that the average absolute relative error (AARE) is less than 0.5%, and coefficient of determination (R2) is more than 0.99 for the overall data. The developed ANN-model covers wide range of pressures and temperatures. Moreover, it covers various NPs’ types, concentrations, and sizes, which confirms its useability and coverability.
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